McLeish was aware of Carroll being eligible to play for Scotland via his grandmother being born north of the border.
But he failed in his attempt - as did current national boss Craig Levein - and Carroll has since played for England, scoring his first international goal last month against Ghana at Wembley.
McLeish said: "Andy Carroll has come on leaps and bounds and I did try and get him to play for Scotland when I was manager.
"I was aware that he had got Scottish connections through his family. He was about 19 at that stage, a reserve player really at Newcastle, and I was quite hot on trying to get him to play for Scotland.
"But unfortunately he said 'no' and we all know what he has already achieved in his career. Certainly since he has gone to Liverpool, he has formed a great partnership with Luis Suarez."
Source: PA
Source: PA